Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster resonances

Abstract

Mapping the strong interaction between Rydberg atoms onto single photons via electromagnetically induced transparency enables manipulation of light at the single-photon level and few-photon devices such as all-optical switches and transistors operated by individual photons. Here we demonstrate experimentally that Stark-tuned Förster resonances can substantially increase this effective interaction between individual photons. This technique boosts the gain of a single-photon transistor to over 100, enhances the non-destructive detection of single Rydberg atoms to a fidelity beyond 0.8, and enables high-precision spectroscopy on Rydberg pair states. On top, we achieve a gain larger than 2 with gate photon read-out after the transistor operation. Theory models for Rydberg polariton propagation on Förster resonance and for the projection of the stored spin-wave yield excellent agreement to our data and successfully identify the main decoherence mechanism of the Rydberg transistor, paving the way towards photonic quantum gates.

Introduction

Rydberg excitations of ultracold atoms1 are currently attracting tremendous attention because of possible applications in quantum computing2,3,4,5 and simulation6,7,8,9,10. One particular aspect is the realization of few-photon nonlinearities mediated by Rydberg interaction11,12,13,14, enabling novel schemes for highly efficient single-photon generation15,16, entanglement creation between light and atomic excitations17, single-photon all-optical switches18 and transistors19,20, single-photon absorbers21 and interaction-induced photon phase shifts22,23. Interacting Rydberg polaritons also enable attractive forces between single photons24, crystallization of photons25 and photonic scattering resonances26. The above experiments and proposals make use of the long-range electric dipole–dipole interaction between Rydberg atoms27,28,29,30,31. A highly useful tool for controlling the interaction are Stark-tuned Förster resonances, where two dipole-coupled pair states are shifted into resonance by a dc32 or microwave33,34 electric field. Förster resonances have been studied by observation of dipole blockade35, line shape analysis36, double-resonance spectroscopy37, excitation statistics38 and Ramsey spectroscopy39,40. Recently, resonant four-body interaction41 and the anisotropic blockade on Förster resonance42 and quasi-forbidden Förster resonances43 have been observed, and Förster resonances between different atomic species have been predicted44. For Rydberg-mediated single-photon transistors, the near-resonance in zero field for specific pair states has been used to enhance the transistor gain20, while in experiments on Rydberg atom imaging45,46 an increase in Rydberg excitation hopping has been observed on resonance47.

In this work, we use Stark-tuned Förster resonances to greatly increase the interaction between individual photons inside a Rydberg medium. We achieve this by tuning pair states |S(g),S(s)〉 containing two different Rydberg S-states into resonance with |P(g),P(s)〉 pair states by an electric field. We show that for gate and source Rydberg states |50S1/2,48S1/2〉, we can boost the performance of a Rydberg single-photon transistor. When operated classically, we achieve , enabling high-fidelity detection of single Rydberg atoms. This improved transistor can be operated such that the gate photon is read out with finite efficiency, reaching a gain . We develop theoretical models for the dynamics of Rydberg polaritons in the presence of Förster resonances and the loss of coherence due to photon scattering. Excellent agreement with our experimental data is found. Finally, our all-optical probe represents a novel approach for the high-resolution study of the substructure of Förster resonances caused by fine structure and Stark/Zeeman splitting of the |P(g),P(s)〉 pair states. We demonstrate this technique by resolving the multi-resonance structure of the |66S1/2,64S1/2〉 pair state.

Results

Experimental set-up

Our experimental scheme13,19,20,45 is shown in Fig. 1a,b: by coupling the excited state |e〉 and the Rydberg state |S(g)〉 with a strong light field Ωg with detuning δg, a gate photon  is converted into a Rydberg excitation inside a cloud of ultracold 87Rb atoms. We then probe the presence of this gate excitation by monitoring the transmission of source photons  coupled via electromagnetically induced transparency (EIT) to the source Rydberg state S(s). Specifically, we use (δg=40 MHz) for efficient Raman absorption of the gate photon in the experiments without retrieval, while we use EIT-based slow light techniques (δg=0) for photon storage in experiments with gate photon retrieval. At zero electric field, the interaction between the |S(g),S(s)〉 pair is of van der Waals type. The difference in electric polarizability between S- and P-states enables the shift of the initial pair state into degeneracy with specific |P(g),P(s)〉 pairs, resulting in resonant dipole–dipole interaction. We shift the Rydberg levels by applying a homogeneous electric field along the direction of beam propagation. Active cancellation of stray electric fields is done with eight electric field plates in Löw configuration48, while the homogeneous field results from additional voltages V+,V− to four electrodes (Fig. 1a).

Figure 1: High-resolution spectroscopy of Förster resonances.

(a) Tightly focussed source and gate beams (w0=6.2 μm) are overlapped with an optically trapped cloud of 2 × 104 87Rb atoms at 3 μK (cylindrical 1/e dimensions L=40 μm, R=10 μm). For each transistor operation the optical trap is shut off for 200 μs. We perform 23 individual experiments in a single cloud, recapturing the atoms in-between with minimal loss and heating. In-vacuum electrodes are used to apply the electric field. (b) Level scheme for gate and source photons coupled to different Rydberg states, where 2Ω is the Rabi frequency of the control field and 2γ is the decay rate of |e〉. (c,d) At certain electric fields (vertical dashed lines), the |S(g),S(s)〉 pair state is resonant to pair states of type |P(g),P(s)〉. The enhancement of interaction between |S(g)〉 and |S(s)〉 manifests in peaking of the transistor gain (blue dots). In c, the fine structure of the involved P-states and the mJ-dependence of the Stark-shift result in the observed multi-resonance structure. The blue solid line is a theoretical analysis of the full-polariton propagation in the presence of the gate excitation. The error bars are the s.e.m.